1. The Kinetic Molecular Model for Gases
Gas consists of large number of small individual particles with negligible size
Particles in constant random motion and collisions
No forces exerted among each other
Kinetic energy directly proportional to temperature in Kelvin

2. Maxwell-Boltzmann Velocity Distribution
M-B Equation gives distribution of molecules in terms of:
Speed/Velocity, and
Energy
One-dimensional Velocity Distribution in the x-direction:
[ 1Du-x ]

3. Mcad

4. Maxwell-Boltzmann Distribution
3D Velocity Distribution: [ 3Du ] , Let: a = m/2kT
Cartesian Coordinates:

5. Maxwell-Boltzmann Speed Distribution
Re-shape box into sphere of same volume with radius u .
V = (4/3)  u with u2 = ux2 + uy2 + uz2
dV = dux duy duz = 4  u2 du

6. 3D Maxwell-Boltzmann Speed Distribution
Low T
High T

7. 3D Maxwell-Boltzmann Speed Distribution
Conversion of Velocity-distribution to Energy-distribution:
 = ½ m u2 ; d  = mu du

8. Velocity Values from M-B Distribution
urms = root mean square velocity
uavg = average velocity
ump = most probable velocity

9. Comparison of Velocity Values
Ratio in terms of :
urms
uavg
ump
1.73
1.60
1.41

10. Fraction of molecules with E > Ea : e-Ea/RT (Maxwell-Boltzmann Distribution)